BCS theory for s+g-wave superconductivity borocarbides Y(Lu)Ni${}_2$B${}_2$C

The s+g mixed gap function \Delta_k=\Delta {[(1-x)-x\sin^4\theta\cos4\phi]} (x: weight of g-wave component) has been studied within BCS theory. By suitable consideration of the pairing interaction, we have confirmed that the coexistence of s- and g-wave, as well as the state with equal s and g amplitudes (i.e., x=1/2) may be stable. This provides the semi-phenomenological theory for the s+g-wave superconductivity with point nodes which has been observed experimentally in borocarbides YNi_2B_2C and possibly in LuNi_2B_2C.